Interest Rate Calculator
You know where you are, where you want to be and how long you have. This solves for the only piece left: the return that gets you there.
The address carries whatever you changed, so anyone opening it sees these numbers. Nothing is saved on our side.
Required annual rate
5.28%
Turning $5,000 plus $200 a month into $40,000 over 10 years needs 5.28% compounded monthly — an APY of 5.41%.
- 5.28%
- as a bank would quote it
- 5.41%
- what to compare between accounts
- $29,000
- $11,000
- $40,000
- 27.5%
What more time is worth
The same target from the same starting point, given longer. Time is the input that lowers the required return, and it lowers it faster than most people expect.
| Time available | Required rate | Total contributed | vs yours |
|---|---|---|---|
| 5 yearsPuts in $17,000 | $25 | −$12,000 less in total | |
| 10 yearsyoursPuts in $29,000 | $5 | — | |
| 15 yearsNo positive rate reaches it | $0 | +$12,000 more in total | |
| 20 yearsNo positive rate reaches it | $0 | +$24,000 more in total | |
| 30 yearsNo positive rate reaches it | $0 | +$48,000 more in total |
If the rate the calculator returns looks implausible, that is the answer: the plan needs more time, more contributions or a smaller target, not a better fund. A required return in the high teens is not a goal — it is a warning.
Nominal rate or APY?
Both are given above, and they answer different questions.
The nominal rate
What a bank puts on the sign, before compounding is taken into account. It depends on how often interest is credited, so two accounts quoting the same nominal rate can pay different amounts. Use it when you are matching a specific quoted rate.
The APY
What the money actually earns in a year, all compounding included. This is the comparable number, and it is why US banks are required to disclose APY on deposit accounts. Use it when you are choosing between two places to put money.
How this calculator works
Two different problems, depending on whether you are adding money along the way.
With a lump sum and nothing added, the rate follows directly from rearranging the compound formula: r = (FV/PV)^(1/t) − 1.
Add monthly contributions and no such rearrangement exists — the rate appears inside a sum of differently-aged terms. So the calculator searches instead: it brackets the answer between a rate that falls short and one that overshoots, and halves the interval repeatedly until the two meet. The ending balance always rises with the rate, which is what makes this both possible and unambiguous.
Contributions are credited at the end of each month, and the growth applied each month is derived from your chosen compounding frequency so the result agrees with how a bank would compute it. The answer is given as a nominal rate and as an APY, because those are different numbers.
What is assumed
- A constant rate for the whole period.
- Contributions of the same amount, every month, at month end.
- Nothing withdrawn along the way.
- No tax, fees or inflation.
A worked example
$5,000 today, $200 a month, and $40,000 wanted in ten years.
| You contribute | $5,000 + ($200 × 120) |
|---|---|
| Target | In ten years |
| Growth must supply | 40,000 − 29,000 |
| Required nominal rate | Compounded monthly |
| The same rate as an APY | (1 + 0.0528/12)¹² − 1 |
| Share of the target that is growth | 11,000 ÷ 40,000 |
5.28% is a demanding but not unreasonable requirement, which makes this a plan rather than a wish. The useful test is what happens when you shorten the time: at five years the same target needs a return no ordinary portfolio delivers, and the honest response is to change the plan rather than to go looking for the return.
Note too that growth is only 27.5% of the ending balance here. Over ten years contributions do most of the work; it is over thirty that the proportions reverse. If the required rate is uncomfortable, more time changes it faster than anything else you control.
Questions people ask
With no contributions it is a rearrangement of the compound formula: r = (FV/PV)^(1/t) − 1. $10,000 growing to $16,288.95 over ten years is (1.628895)^0.1 − 1 = 5%. Once regular contributions are involved there is no closed form at all, and the answer has to be found numerically — which is what this calculator does.
By bisection. The ending balance is strictly increasing in the rate, so the calculator brackets the answer between a rate that undershoots and one that overshoots, then halves the interval two hundred times. That the balance always rises with the rate is what guarantees the answer is unique — there is exactly one rate that produces your target, not several.
Use the APY to compare accounts and the nominal rate to match a specific quote. A nominal rate depends on how often interest is credited, so two accounts advertising the same nominal rate can pay different amounts; the APY folds that in and is directly comparable. Both are given above for exactly this reason.
It means the plan does not work, and that is the useful answer. A required return in the high teens is not a target to go looking for — it is a signal that the goal needs more time, larger contributions, or to be smaller. Reaching for a return to close a gap is how people end up in products that promise one.
Because the target is below what you would contribute. If you put in $29,000 over ten years and want to end with $25,000, no positive return does that — only a loss would. Check the figures: it is usually a target entered as a monthly amount, or contributions entered annually.
Not directly. This solves for a growth rate on money you hold, where contributions add to a balance. A loan runs the other way, with payments reducing a balance, and the equivalent figure there is the APR — the APR Calculator handles that, including the fees that a loan's stated rate leaves out.
Related calculators
A required rate is not a forecast. It says what a plan needs, not what any investment will deliver, and it does not account for tax, fees, inflation or the fact that real returns arrive unevenly.